Square Root of 115
2026-02-28 17:53 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-115

This is a method used for obtaining the square root for non-perfect squares. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 115:


 Step 1 : Write the number 115, and draw a horizontal bar above the pair of digits from right to left.


Step 2 : Now, find the greatest number whose square is less than or equal to 1. Here, it is 1, Because 12=1 < 1.


Step 3 : Now divide 1 by 1 such that we get 1 as quotient and then multiply the divisor with the quotient, we get 1


Step 4: Subtract 1 from 1. Bring down 1 and 5 and place it beside the difference 0.


Step 5: Add 1 to same divisor, 1. We get 2.


Step 6: Now choose a number such that when placed at the end of 2, a 2-digit number will be formed. Multiply that particular number by the resultant number to get a number less than 1. Here, that number is 0. 
20×0=0<1.


Step 7: Subtract 15-0=15. Add a decimal point after the new quotient 10, again, bring down two zeroes and make 15 as 1500. Simultaneously add the unit’s place digit of 20, i.e., 0 with 20. We get here, 20. Apply Step 5 again and again until you reach 0. 

We will show two places of precision here, and so, we are left with the remainder, 17271 (refer to the picture), after some iterations and keeping the division till here, at this point 

              Step 8 : The quotient obtained is the square root. In this case, it is 10.723….